What is (ln(n)-2ln(Θ))/(2ln(n)) ?

The solution to (ln(n)-2ln(Θ))/(2ln(n)) is (ln(n/(Θ^2)))/(2ln(n))

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simplify (ln(n)-2ln(Θ))/(2ln(n))

simplify

\frac{ln ( n ) - 2 ln ( Θ )}{2 ln ( n )}

\frac{ln ( \frac{n}{Θ ^{2}} )}{2 ln ( n )}

Solution steps

\frac{ln ( n ) - 2 ln ( Θ )}{2 ln ( n )}

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (Θ) = ln (Θ^{2})

= \frac{ln ( n ) - ln ( Θ ^{2} )}{2 ln ( n )}

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (n) - ln (Θ^{2}) = ln (\frac{n}{Θ ^{2}})

= \frac{ln ( \frac{n}{Θ ^{2}} )}{2 ln ( n )}

lo g_{e} (\frac{2 x - 1}{x - 1})

lo g_{e} (0.4 p) - lo g_{e} (p)

3 [2 ln (x - 1) - ln (x)] + ln (x + 1)

\frac{1}{8} ln (2)

ln (0.00006) - ln (0.00022)

What is (ln(n)-2ln(Θ))/(2ln(n)) ?
The solution to (ln(n)-2ln(Θ))/(2ln(n)) is (ln(n/(Θ^2)))/(2ln(n))